Placing Fields

To set the scene, I am a one day old Orchard newbie. My initial experiences are very positive and I have found the documentation and videos very helpful, but...

There is one aspect (so far) that I can't seem to address or find reference to. Here is the scenario:

I am using 'The Theme Machine' theme and I want all of my pages to define, let's say, two blocks of HTML content; one in the Content region (the body HTML) and one in say the AsideFirst Region.

I have added a new Text field to my Page's Content Definition and set its flavour to Html. Sure enough, when I edit/create a page I get two HTML editors, but I can't figure out how I can move the new HTML field into a different region (AsideFirst) of the theme.
I tried Edit Placement in the Page's Content Definition, but this only seems to allow me re-order the fields, not relocate them.

I have been able to emulate what I want to do by creating a Widget and assigning it to the default layer, but then I seem to get the same text on every page, when what I want to be able to do is have page specific bespoke AsideFirst HTML mark-up on each page.

I'm guessing that I am missing something or using the wrong technique, but I've run out of ideas.